Difference between revisions of "2021 USAJMO Problems/Problem 1"
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After 2, all primes are odd, and the average of 2 and 3 is not an integer. | After 2, all primes are odd, and the average of 2 and 3 is not an integer. | ||
| − | We proceed with mod 4. The 2 primes must be equivalent mod 4. | + | We proceed with mod 4. The 2 primes must be equivalent mod 4 because their difference cannot be 2 or 6 because that does not work. |
Revision as of 12:32, 13 April 2021
Problem
Find all primes, with proof, that are the average of 2 consecutive primes.
Solution
After 2, all primes are odd, and the average of 2 and 3 is not an integer.
We proceed with mod 4. The 2 primes must be equivalent mod 4 because their difference cannot be 2 or 6 because that does not work.
